Nuprl Lemma : member-interface-predecessors-subtype
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀e:E(X). ∀e':{a:E(X)| loc(a) = loc(e) ∈ Id} . ((e' ∈ ≤(X)(e)) ⇐⇒ e' ≤loc e )
Proof
Definitions occuring in Statement :
es-interface-predecessors: ≤(X)(e),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-loc: loc(e),
Id: Id,
l_member: (x ∈ l),
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
set: {x:A| B[x]} ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
es-E-interface: E(X),
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
prop: ℙ,
rev_implies: P ⇐ Q,
uimplies: b supposing a,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}e:E(X). \mforall{}e':\{a:E(X)| loc(a) = loc(e)\} .
((e' \mmember{} \mleq{}(X)(e)) \mLeftarrow{}{}\mRightarrow{} e' \mleq{}loc e )
Date html generated:
2016_05_17-AM-07_00_09
Last ObjectModification:
2015_12_29-AM-00_13_35
Theory : event-ordering
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